Independent Uniform Distributions Research Articles

Calibration of high-fidelity hydrodynamic models utilizing on-site vessel response measurements

With a focus on weather-restricted marine operations, a comprehensive work on numerical model calibration is conducted to improve the vessel response prediction accuracy in real environmental conditions. This framework involves using existing physics-based models in which the metocean and system parameters are entered as inputs to derive vessel responses. The numerical models based on linear potential flow theory resolve only a part of the physics, i.e., it does not account for viscous damping effects. Moreover, significant uncertainties are associated with the system parameters related to the vessel operational conditions that are not known or measured directly. Therefore, the present paper integrates the vessel model with a derivative-free Lipschitz optimization technique to calibrate the vessel system parameters. For efficient optimization, the most influential variables are identified by conducting a sensitivity study for relevant quantities of interest using a cost-effective Polynomial Chaos model. The sensitivity analysis assumes independent uniform distributions for the system parameters with proper lower and upper limits. Subsequently, estimates of the highly influential variables are optimized using on-site vessel measurements, and in turn, utilized for superior response estimation. The response computations based on the numerical wave spectrum produced superior results in comparison with the results based on the parametric wave spectrum. The calibration algorithm is validated with full-scale measurements using frequency and time domain approaches for simulating vessel motions. It has been quantitatively revealed that the Center of Gravity parameters associated with the vessel operational characteristics and sea state-dependent additional damping coefficients govern the Roll response variation to a great extent. The calibration of these parameters resulted in improved Roll spectra estimations that match the measured spectra closely.

Uniform distributions and random variate generation over generalized [formula omitted] balls and spheres

This paper studies a class of distributions supported on generalized balls and spheres that are extensions of lp balls and spheres, defined based on power-sum polynomials—which can be non-symmetric. The joint, marginal, and conditional distributions corresponding to these distributions are presented. Then, three stochastic representations are developed based on independent uniform distributions, multivariate Dirichlet distributions, and independent generalized normal (Gaussian) distributions. The sampling schemes developed based on these representations are numerically compared. Moreover, it is shown that the distributions of any two associated generalized lp ball and sphere can be represented based on each other. It is observed that the proposed distributions over generalized lp balls are uniform with respect to the Lebesgue measure. However, except in the case of lp spheres, the distribution over a generalized lp sphere is not uniform with respect to the corresponding cone measure (a disintegration of the Lebesgue measure on the associated generalized ball). Using our results, a procedure is provided for uniform sampling over generalized-sphere manifolds with respect to the Hausdorff measure—which is known as the natural surface-area measure. The proposed distributions can be used to define new classes of distributions and copulas that can be sampled efficiently. Moreover, our results pave the way to define flexible and manageable uncertainty sets in robust optimization, or in analysis and control of uncertain systems.

A new approach for group decision making method with hesitant fuzzy preference relations

This paper focuses on group decision making with hesitant fuzzy preference relations (HFPRs). To derive the consistent ranking order, a new multiplicative consistency concept for HFPRs is introduced that considers all information offered by the decision makers. The main feature is that this concept neither adds values to hesitant fuzzy elements nor disregards any information provided by the decision makers. To judge the multiplicative consistency of HFPRs, 0–1 mixed programming models are constructed. According to the assumption that there is an independent uniform distribution on values in hesitant fuzzy elements, the hesitant fuzzy priority weight vector is derived from multiplicative consistent reciprocal preference relations and their probabilities. Meanwhile, several consistency based 0–1 mixed models to estimate missing values in incomplete HFPRs are constructed that can address the situation where ignored objects exist. Considering the consensus in group decision making, a distance measure based consensus index is defined, and a method for improving the group consensus is provided to address the situation where the consensus requirement is unsatisfied. Then, a distance measure between any two HFPRs is introduced that is used to define the weights of the decision makers. Furthermore, a multiplicative consistency and consensus based interactive algorithm for group decision making with HFPRs is developed. Finally, a multi-criteria group decision making problem with HFPRs is offered to show the concrete application of the procedure, and comparison analysis is also made.

A comment on “computational complexity of stochastic programming problems”

Although stochastic programming problems were always believed to be computationally challenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Math Program A 106(3):423---432, 2006). Amongst others, that paper argues that linear two-stage stochastic programs with fixed recourse are #P-hard even if the random problem data is governed by independent uniform distributions. We show that Dyer and Stougie's proof is not correct, and we offer a correction which establishes the stronger result that even the approximate solution of such problems is #P-hard for a sufficiently high accuracy. We also provide new results which indicate that linear two-stage stochastic programs with random recourse seem even more challenging to solve.

When the a contrario approach becomes generative

The a contrario approach is a statistical, hypothesis testing based approach to detect geometric meaningful events in images. The general methodology consists in computing the probability of an observed geometric event under a noise model (null hypothesis) $$H_0$$H0 and then declare the event meaningful when this probability is small enough. Generally, the noise model is taken to be the independent uniform distribution on the considered elements. Our aim in this paper will be to question the choice of the noise model: What happens if we "enrich" the noise model? How to characterize the noise models such that there are no meaningful events against them? Among them, what is the one that has maximum entropy? What does a sample of it look like? How is this noise model related to probability distributions on the elements that would produce, with high probability, the same detections? All these questions will be formalized and answered in two different frameworks: the detection of clusters in a set of points and the detection of line segments in an image. The general idea is to capture the perceptual information contained in an image, and then generate new images having the same visual content. We believe that such a generative approach can have applications for instance in image compression or for clutter removal.

Reliability Estimators for the Components of Series and Parallel Systems: The Weibull Model

This paper presents a hierarchical Bayesian approach to the estimation of components' reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival censored data, because the estimation of a component's reliability in a series (parallel) system is equivalent to the estimation of its survival function with right- (left-) censored data. Besides the Weibull parametric model for reliability data, independent gamma distributions are considered at the first hierarchical level for the Weibull parameters and independent uniform distributions over the real line as priors for the parameters of the gammas. In order to evaluate the model, an example and a simulation study are discussed.

Mathematical properties of the [formula omitted] measure of linkage disequilibrium

Statistics for linkage disequilibrium (LD), the non-random association of alleles at two loci, depend on the frequencies of the alleles at the loci under consideration. Here, we examine the r 2 measure of LD and its mathematical relationship to allele frequencies, quantifying the constraints on its maximum value. Assuming independent uniform distributions for the allele frequencies of two biallelic loci, we find that the mean maximum value of r 2 is ∼0.43051, and that r 2 can exceed a threshold of 4/5 in only ∼14.232% of the allele frequency space. If one locus is assumed to have known allele frequencies–the situation in an association study in which LD between a known marker locus and an unknown trait locus is of interest–we find that the mean maximum value of r 2 is greatest when the known locus has a minor allele frequency of ∼0.30131. We find that in 1/4 of the space of allowed values of minor allele frequencies and haplotype frequencies at a pair of loci, the unconstrained maximum r 2 allowing for the possibility of recombination between the loci exceeds the constrained maximum assuming that no recombination has occurred. Finally, we use r max 2 to examine the connection between r 2 and the D ′ measure of linkage disequilibrium, finding that r 2 / r max 2 = D ′ 2 for ∼72.683% of the space of allowed values of ( p a , p b , p a b ) . Our results concerning the properties of r 2 have the potential to inform the interpretation of unusual LD behavior and to assist in the design of LD-based association-mapping studies.

Distributions of Invariant Ensembles from the Classical Orthogonal Polynimials: the Discrete Case

We examine the Charlier, Meixner, Krawtchouk and Hahn discrete orthogonal polynomial ensembles, deeply investigated by K. Johansson, using integration by parts for the underlying Markov operators, differential equations on Laplace transforms and moment equations. As for the matrix ensembles, equilibrium measures are described as limits of empirical spectral distributions. In particular, a new description of the equilibrium measures as adapted mixtures of the universal arcsine law with an independent uniform distribution is emphasized. Factorial moment identities on mean spectral measures may be used towards small deviation inequalities on the rightmost charges at the rate given by the Tracy-Widom asymptotics.

A model for velocity fluctuations in sedimentation

We present a model for velocity fluctuations of dilute sedimenting spheres at low Reynolds number. The central idea is that a vertical stratification causes the fluctuations to decrease below those of an independent uniform distribution of particles, such a stratification naturally occurring from the broadening of the sedimentation front. We use numerical simulations, scaling arguments, structure factor calculations, and experiments to show that there is a critical stratification above which the characteristics of the density and velocity fluctuations change significantly. For thin cells, the broadening of the sediment front (and the resulting stratification) is small, so the velocity fluctuations are predicted by independent-Poisson-distribution estimates. In very thick cells, the stratification is significant, leading to persistent decay of the velocity fluctuations for the duration of the experiment. Estimated stratifications quantitatively agree with the simulations, and indicate the likelihood that previous experimental measurements were also affected by stratification. The velocity fluctuations in sedimentation are therefore not universal but instead depend on both the cell shape and developing stratification.

Differential Operators and Spectral Distributions of Invariant Ensembles from the Classical Orthogonal Polynomials. The Continuous Case

Following the investigation by U. Haagerup and S. Thorbjornsen, we present a simple differential approach to the limit theorems for empirical spectral distributions of complex random matrices from the Gaussian, Laguerre and Jacobi Unitary Ensembles. In the framework of abstract Markov diffusion operators, we derive by the integration by parts formula differential equations for Laplace transforms and recurrence equations for moments of eigenfunction measures. In particular, a new description of the equilibrium measures as adapted mixtures of the universal arcsine law with an independent uniform distribution is emphasized. The moment recurrence relations are used to describe sharp, non asymptotic, small deviation inequalities on the largest eigenvalues at the rate given by the Tracy-Widom asymptotics.

A Probabilistic Minimax Location Problem on the Plane

In this paper we consider the weighted minimax (1-center) location problem in the plane when the weights are not given but rather drawn from independent uniform distributions. The problem is formulated and analyzed. For certain parameters of the uniform distributions the objective function is proven to be convex and thus can be easily solved by standard software such as the Solver in Excel. Computational experience is reported.

Comparison of tests for bivariate normality with unknown parameters by transformation to an univariate statistic

Fifteen tests for bivariate normality with unknown parameters have been compared. A Monte Carlo power analysis with componently independent uniform, lognormal and Student t4 distributions and with members of the family of bivariate gamma distributions as alternative hypothesis has been carried out. The Shapiro-Wilk- Stephens test has been found to perform well for all alternative distributions analyzed. The Shapiro-Wilk- Malkovich and Malkovich bl tests exhibit good power against the lognormal and the family of bivariate gamma distributions, but show poor power against independent uniform distributions. The bivariate test methods have been illustrated for the strength and elongation at break of Dyneema polyethylene yarn and nylon 6 monofilament. Dyneema is a trademark of DSM.

Point processes with a conditionally independent uniform distribution of points on intervals

Point processes with a conditionally independent uniform distribution of points on intervals

Obtaining a Normal Sequence with Prescribed Covariances from an Independent Uniform Distribution of Random Variables

Obtaining a Normal Sequence with Prescribed Covariances from an Independent Uniform Distribution of Random Variables